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Fuzzy controller theory: Limit theorems for linear fuzzy control rules. (English) Zbl 0685.93003
Summary: For a general fuzzy controller employing linear fuzzy control rules it is shown that as the number of rules grow the defuzzified output becomes a linear function of the input. In particular, for a sufficiently large number of rules, the defuzzified output is approximately the same as the PI (PID) controller.

MSC:
93A10 General systems
93C05 Linear systems in control theory
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[1] Buckley, J.J.; Ying, H., Linear fuzzy controller: it is a linear non-fuzzy controller, Inf. sci., (1989), to be published · Zbl 0685.93003
[2] Siler, W.; Ying, H., Fuzzy control theory: the linear case, Fuzzy sets systems, (1989), to be published · Zbl 0683.93002
[3] Ying, H.; Siler, W.; Buckley, J.J., Fuzzy control theory: a nonlinear case, () · Zbl 0937.03031
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